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On the difference between the Szeged and the Wiener index

Author

Listed:
  • Bonamy, Marthe
  • Knor, Martin
  • Lužar, Borut
  • Pinlou, Alexandre
  • Škrekovski, Riste

Abstract

We prove a conjecture of Nadjafi-Arani et al. on the difference between the Szeged and the Wiener index of a graph (Nadjafi-Aranifi et al., 2012). Namely, if G is a 2-connected non-complete graph on n vertices, then Sz(G)−W(G)≥2n−6. Furthermore, the equality is obtained if and only if G is the complete graph Kn−1 with an extra vertex attached to either 2 or n−2 vertices of Kn−1. We apply our method to strengthen some known results on the difference between the Szeged and the Wiener index of bipartite graphs, graphs of girth at least five, and the difference between the revised Szeged and the Wiener index. We also propose a stronger version of the aforementioned conjecture.

Suggested Citation

  • Bonamy, Marthe & Knor, Martin & Lužar, Borut & Pinlou, Alexandre & Škrekovski, Riste, 2017. "On the difference between the Szeged and the Wiener index," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 202-213.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:202-213
    DOI: 10.1016/j.amc.2017.05.047
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    Cited by:

    1. Wang, Guangfu & Li, Shuchao & Qi, Dongchao & Zhang, Huihui, 2018. "On the edge-Szeged index of unicyclic graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 94-106.
    2. Ji, Shengjin & Liu, Mengmeng & Wu, Jianliang, 2018. "A lower bound of revised Szeged index of bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 480-487.
    3. Hriňáková, Katarína & Knor, Martin & Škrekovski, Riste, 2019. "An inequality between variable wiener index and variable szeged index," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Yao, Yan & Ji, Shengjin & Li, Guang, 2020. "On the sharp bounds of bicyclic graphs regarding edge Szeged index," Applied Mathematics and Computation, Elsevier, vol. 377(C).

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